x2+3x+1=0,求x3+1/x3与x7+1/x7的值.

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x2+3x+1=0,求x3+1/x3与x7+1/x7的值.
x2+3x+1=0,求x3+1/x3与x7+1/x7的值.

x2+3x+1=0,求x3+1/x3与x7+1/x7的值.
x^2+3x+1=0,求x^3+1/x^3与x^7+1/x^7的
x^2+3x+1=0 x不等于0
两边同时除以x
x+1/x=-3
x^3+1/x^3=(x+1/x)(x^2-1+1/x^2)=3[(x+1/x)^2-3]=3*[(-3)^2-3]=18
x^2+1/x^2=7
平方
x^4+2+1/x^4=49
x^4+1/x^4=47
x^7+1/x^7
=(x^4+1/x^4)(x^3+1/x^3)-x^4*1/x^3-x^3*1/x^4
=(x^4+1/x^4)(x^3+1/x^3)-(x+1/x)
=47*(-18)-(-3)
=-843

∵x2+3x+1=0
∴x+1/x=-3(将原式除以x)
∴（x+1/x）^2=9
∴x^2+1/x^2=7
∴x^3+1/x^3=(x+1/x)(x^2-x*1/x+1/x^2)=-18
∴x^4+1/x^4=(x^2+1/x^2)^2-2=47
∴x^7+1/x^7=(x^3+1/x^3)(x^4+1/x^4)-(x+1/x)=-843
∴x^3+1/x^3=-18
x^7+1/x^7=-843

x^2+3x+1=0，
x^2+1=-3x
两边除以x
x+1/x=-3
平方
x^2+2+1/x^2=9
x^2+1/x^2=7
1、
x^3+1/x^3
=(x+1/x)(x^2-1+1/x^2)
=-3*(7-1)
=-18
2、
x^2+1/x^2=7
平方
x^4+2+...

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x^2+3x+1=0，
x^2+1=-3x
两边除以x
x+1/x=-3
平方
x^2+2+1/x^2=9
x^2+1/x^2=7
1、
x^3+1/x^3
=(x+1/x)(x^2-1+1/x^2)
=-3*(7-1)
=-18
2、
x^2+1/x^2=7
平方
x^4+2+1/x^4=49
x^4+1/x^4=47
x^7+1/x^7
=(x^4+1/x^4)(x^3+1/x^3)-x^4*1/x^3-x^3*1/x^4
=(x^4+1/x^4)(x^3+1/x^3)-(x+1/x)
=47*(-18)-(-3)
=-843

收起

-18
-843

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